Now Rizzo if you had covered that you are an outdoor person I could have tailored my response to that the first time around!

Mountain biking - I am going to assume since you are traveling and you won't have a bike with you? If that's the case, Bike Mart can rent you a mountain bike. I would call to reserve one though. Their website which includes their locations and prices is www.bikemart.com. Where to go moutain biking? You didn't indicate your level so it's hard to recommend one specific trail. Here the website for Dorba, www.dorba.org, Dallas Off Road Bicycle Association. They have trail conditions, maps, difficulty levels and more importantly if the trail is closed. We have a lot of mountain biking trails closed in the DFW area because of the rains. Lake Grapevine has a popular off road trail but it's flooded. Bike Mart can help direct you to a good trail based on existing conditions.

Parks - Here is the website for local Texas state parks, http://www.tpwd.state.tx.us/. Lake Mineral Well is a state park, has riding trails and scenic in a Texas sort of way. http://www.tpwd.state.tx.us/spdest/f...mineral_wells/
There aren't any national parks that I am aware of within 100+ miles of DFW, http://www.nps.gov/findapark/index.htm# so you may have a drive for that.

Hiking - DFW Outdoors will have hiking trips that are open to the public. http://www.texasoutside.com/hikebike/. I don't hike much in Texas, I can't recommend where to go hiking here, I go to Colorado. I just got back from a hiking trip in the Rocky Mountain and Roosevelt Mountains in Colorado. I prefer hiking in Colorado to hiking in Texas, no rattlesnakes, no fire ants, no plants that shred my delicate skin, no mosquitos, no chiggers and usually a perfect 68 degrees when it's 105 degrees back home in Texas during the summer.